1. Field of the Invention
This invention relates generally to a method and apparatus for determining the shape and orientation of a borehole traversing an earth formation and the motion of a tool within the borehole while drilling the borehole. More specifically, this invention relates to a nonlinear parameter estimation technique used to approximate the shape of an earth borehole by measuring the distance from the tool to the borehole wall at a plurality of locations around the periphery of the tool and fitting those measured distances to a predetermined shape function in such a manner as to minimize the error between the estimated shape and the measured distances.
2. Description of the Related Art
The cross-sectional shape of a borehole traversing an earth formation is useful in ascertaining other valuable information regarding various properties of the formation, such as stress, porosity, and density. Several methods to obtain information about the shape of a borehole are described in U.S. Pat. No. 5,469,736 to Moake, U.S. Pat. No. 5,638,337 to Priest, U.S. Pat. No. 5,737,277 to Priest, and references cited therein, each of which is incorporated herein by reference. Such methods generally employed acoustic or mechanical calipers to measure the distance from the tool to the borehole wall at a plurality of points around the perimeter of the tool.
However, the method described in the '736 patent appears to be based on the assumption that the borehole shape is circular, or at least that the shape may be approximated by an "equivalent" circle, i.e., a circle having an area equivalent to that of the actual borehole. A significant drawback to that method is that, in reality, the borehole shape is often not circular but is rather of an elliptical or even more complex shape. Therefore, under many circumstances, that method does not accurately describe the true borehole shape. Furthermore, although the methods described in the '337 and '277 patents do account for the ellipticity of a borehole and tool rotation during measurement, those methods assume that the tool does not translate in the borehole during measurement. During drilling operations, however, the tool is rarely free from translational motion. Thus, those methods generally do not provide satisfactory results in a measuring while drilling (MWD) mode of operation. Additionally, the '337 and '277 patents do not account for borehole shapes that are more complex than an ellipse.
Regarding the motion of a rotating tool within a borehole, U.S. Pat. No. 4,958,125, issued Sep. 18, 1990, to Jardine et al., discloses a method and apparatus for determining the lateral acceleration of the tool using accelerometers. As discussed below, the method of the '125 patent is directed to a vertical drill string orientation and does not account for the contribution of gravity to the accelerometer signals. However, in modern petroleum well drilling and logging, the drill string is frequently not in a vertical orientation. Thus, the method and apparatus of the '125 patent does not solve a significant problem in the art.
It would, therefore, be a significant advance in the art of petroleum well drilling and logging to provide a method and apparatus for accurately determining the shape and orientation of an elliptical or more complex earth borehole and the motion of a tool therein while drilling the borehole in any general inclined direction.